Boolean algebras with no rigid or homogeneous factors
Author:
Petr Štěpánek
Journal:
Trans. Amer. Math. Soc. 270 (1982), 131147
MSC:
Primary 06E05; Secondary 03E40
MathSciNet review:
642333
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Abstract: A simple construction of Boolean algebras with no rigid or homogeneous factors is described. It is shown that for every uncountable cardinal there are isomorphism types of Boolean algebras of power with no rigid or homogeneous factors. A similar result is obtained for complete Boolean algebras for certain regular cardinals. It is shown that every Boolean algebra can be completely embedded in a complete Boolean algebra with no rigid or homogeneous factors in such a way that the automorphism group of the smaller algebra is a subgroup of the automorphism group of the larger algebra. It turns out that the cardinalities of antichains in both algebras are the same. It is also shown that every distributive complete Boolean algebra can be completely embedded in a distributive complete Boolean algebra with no rigid or homogeneous factors.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198206423333
PII:
S 00029947(1982)06423333
Keywords:
Boolean algebras with no rigid or homogeneous factors,
automorphisms,
embeddings and isomorphism types of BA's,
chain conditions,
distributivity
Article copyright:
© Copyright 1982
American Mathematical Society
